Chosen answer:He never strictly gives up, he just realises the practicalities of the situation, that it took Red Dwarf three million years to get to where it is, so it would take the same length of time to return. While he originally plans to go back into stasis for the long journey, the "future echoes" that he sees while travelling at light speed convince him that he should stay active on board the ship instead and look for alternative ways to get back, something that influences the plot of several subsequent episodes.

Chosen answer:He brought Rimmer back because he's the person that Lister had the most interaction with during his time on Red Dwarf and also because all Lister ever did with his friends was get very drunk. Lister may not like Rimmer, but bringing him back probably has the best chance of keeping him relatively sane.

Chosen answer:It can, but that doesn't mean that it's supposed to. At the time of the episode, Red Dwarf's thrusters have been firing continuously for millions of years, accelerating the ship until, in this episode, it finally achieves light speed. This is not a speed that the Dwarf was ever intended to attain, hence the need to slow it down again before the stresses tear it apart. If they wanted to hit light speed again, it would take the same sort of length of time to accelerate back up to that speed. Technically possible, but not exactly practical.

Kryten tells everyone that the matter paddle transmits matter in digital form from one place to another at the speed of light - he is very clear on this point. He then locates Waxworld, which is 200,000 light years away. Okay - so when they use the matter paddle to transmit themselves to Waxworld, why doesn't it take them 200,000 years to get there?